Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.

翻译：扩散过程是一类随机微分方程，在动态建模任务中自然产生丰富的表达性模型族。在生成模型中，当潜过程具有非线性扩散过程先验时，其概率推断与学习是难解问题。我们基于变分推断领域的工作，将后验过程近似为线性扩散过程，并指出该方法的病态特性。我们提出一种替代的高斯变分过程参数化方法，采用基于站点指数族描述。这使得我们能够将使用不动点迭代的慢速推断算法，转换为类似自然梯度下降的凸优化快速算法，该算法还为学习模型参数提供了更优的目标函数。